PFC/JA-93-26
Anomalous Behaviour in ICCS
L. Bromberg, M. Takayasu and J. H. Schultz
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
October 1993
Supported by U. S. Department of Energy through Princeton Plasma Physics
Laboratory Subcontract S-03528-G.
To be published in the Proceedings of the 15th Symposium on Fusion Engineering,
Hyannis, Massachusetts, October 11-15, 1993.
ANOMALOUS BEHAVIOUR IN ICCS
*
L. Bromberg, M. Takayasu and J.H. Schultz
Massachusetts Institute of Technology, Cambridge MA 02139
Abstract
ICCS conductors behave anomalously.
The analysis deals mainly with the unpressurized pool
boiling cases, but the model can be extended to supercritical helium.
Section 2 describes the variations of He fraction across
the cable and their implications. Section 3 describes the
models used to calculate the AC losses. Section 4 describes the experimental results and their analysis. Section 5 describes the implication of the results to supercritical He.
Several anomalies have been documented: quenches
driven by pulsig fields (referred to as ramp-rate
limtations), and energy margins that show a transition between a "well-cooled" and an "ill-cooled"
regime (marking a transition between high energy
margin at low transport current and low energy
margin at higher currents). In this paper, a novel
model will be described that attempts to interpret
experimental data. In the experiments, 3 x 3 x 3
ICCS NbsSn sample coils have been tested for stability to ramping fields and transport currents.
Three such coils have been tested, one made of
triplets made of all SC strands, a second with one
copper and two SC strands and a third one with
one steel and two SC strands. The analysis deals
mainly with unpressurized cases, but the model
also applies to supercritical He. The hypothesis
is that non-uniform helium and superconductor
distribution in the conductor is the cause of the
"anomalous" behaviour. The energy margin as a
function of the transport current has also been
calculated, and it shows a transition. The limiting
current is determined by the highest local fraction
of bunching (averaged over a cross section). The
model, however, has difficulty explaining multiple
ramps.
1
2
Helium fraction
The helium fraction in the conductor refers to the void
volume divided by the total conductor volume. However,
large local differences in helium fraction exist. The minimum fraction occurs when the strands are touching (tight
strands, see Figure 1), resulting in the minimum void fraction
Fuemin =
2
2 - 2 7ra
/2
7ra /2
_10%
where a is the strand radius. Typical average helium fractions are about 4 times larger, i.e. FHe,ave _ 40 %.
Typical
minimal
helium unit
Minimum
helium Area
INTRODUCTION
ICCS conductors behave anomalously when subject to
magnetic field and current variations. In this paper, the
assumption that the non-uniform distribution of helium
and conductor in the cable is the cause of the anomalous
behaviour is tested experimentally and analytically. Two
types of anomalies of ICCS will be addressed in this memorandum: the ramp rate limitations (quenching at lower
ramp rates than would be expected) and energy margin.
The model hypothesizes that if the energy released in
tightly bunched strands exceeds a lower critical limit, the
helium in the tight "channels" vaporizes and the strands
in the tight bunches quench. The current in these strands
is transferred to the loosely bunched strands (with a large
local helium fraction) that are still superconducting. If
the current in these superconducting strands is larger than
their critical current, then the entire conductor quenches.
Strand
Figure 1: Schematic diagram of tightly bunched strands
Helium has very small heat thermal conductivity, k _
0.02 W/mK. The thermal equilibration time in helium is
long, even in the case of supercritical helium:
pca2
1
In the case of pool boiling (unpressurized helium) it is
assumed that the bubbles remain trapped by the strands,
especially in the crevices between strands, as shown in
Figure 1. The helium in these crevices experiences the
largest temperature rise, since the helium fraction is the
smallest and the heating input is the largest (due to the
*This work was supported by DoE through PPPL subcontract
S-03528-G
1
largest metal fraction). Surface tension prevents the small
bubbles formed in the crevices from leaving the system
in the time scale of interest. The expansion of helium
as it goes into the gas phase results in the expulsion of
liquid helium to compensate for the volume increase of
gaseous helium, as shown in Figure 2. The hot helium
flow could be either in the gas or in the liquid phases
(supercritical helium will be discussed below). After the
channels are filled with gaseous helium, any additional
heating to the wires will result in the local quenching of
the superconductor (since the conductor has very little
heat capacity).
These losses are for a full cycle. In order to account for
the quarter cycle, this equation needs to be multiplied by
1/4.
The losses are for a single strand, and many strands can
result in non-uniform losses. This is due to the presence of
fields external to the strands. Both larger and lower losses,
locally, are possible (if the strands are aligned with the
magnetic field, the losses are smaller; if they are aligned
orthogonally to the magnetic field, the losses are larger).
The coupling losses are given by
B 2 28
E,
=
-
-
1o Tramp
Hot He Flow, from
radially inward expansion
Cold He flow,
pushed out by
radially flowing He
Figure 2: Schematic diagram of cold helium expulsion
from tight strands when helium in crevices expands radially inward
Helium experiences an increase in volume of a factor of
8 as it goes from the liquid phase into the gas phase at
1 bar. This means that it is only necessary to evaporate
about 12% of the helium in order for gaseous helium to
totally occupy the volume in between strands.
Using this information, it is possible to evaluate the
parameters for filling 100% of the channel by the gaseous
phase. Atmospheric helium evaporates with 20400 J/kg.
Its liquid density is 125 kg/M 3 . The helium vaporization
energy is therefore 2.5 J/cm3 . Since evaporating only 1/8
of the helium in the channel results in totally filling the
channel with helium gas, the energy needed to fill the
tightly bunched channels with gaseous helium is then 0.3
J/cm 3 . The local heating EHe,iocal with non-uniform void
fraction can be shown to be
3.1 Hysteretic effects
The hysteresis losses depend on the previous history of
the superconductor. Typical hysteretic loops for the DPC
wire are shown in Figure 3 [4]. For the ramp experiments, the hysteretic losses will be different depending
on whether the superconductor starts at point A (unmagnetized), point B (negatively magnetized) or point
C (positively magnetized). For the sets of unipolar field
experiments [1], the magnetic field does not reverse, only
ramps-up and down.
-W
External Field (ke
-40
0
40
ao
4 20A
-O
-.0
.
4
xteraiField (MA/nm)
FHe,ave 1 - Fejocal
Ee,oca1 = Eue,ave FHe,jocal 1 - FHe,ave
-
Figure 3: Hysteresis loop for DPC wire
where FHe,ave and FHeLocaj are the average and the local
helium fraction, and EHeave is the average heat input to
the helium. It is assumed that the heat is generated uniformly in the metal. If FM,
40% and Fn
e, j,n t
.,,,v, - 0 a d
10%, then EHe,ave o EHe,min/ 6 . For EHe,min _ 0.3
J/cm3 (required to fill the tightly bunched channels with
gaseous helium), EHe,ave - 50 mJ/cm3 (energy margin
over the conductor of - 25 mJ/cm3 ). This implies very
small energy margins for the regions with tight strands.
3
E varies for different cable composition and construction
and also may vary longitudinally along the cable.
Non-uniform coupling losses could also exist. Nonuniform losses (both hysteretic and coupling) could be
the explanation of the anomaly.
Hysteretic and Coupling Losses
The hysteresis losses in the DPC strands are given by
Ehs, = 178.2 (1 - e- 0 .21 3 ) x (1 + f2) mW/cm 3
2
The heat dissipated for a unipolar cycle (rampup/ramp-down) is 42% of the losses for the (bipolar) cycle [3]. For the bipolar cycle, about 25% of dissipation
occurs in each quadrant. As shown in Figure 3, the dissipation for the ramp-down in the unipolar cycle is equiva,
lent to the the dissipation in the ramp-down in the bipolar cycle, and approximately 25% of the dissipation for
the full cycle. Therefore, the dissipation during ramp-up
from the unipolar cycle are much lower than those of the
full cycle. The power dissipation during the ramp-up for
the unipolar are 17% of the dissipation in the full bipolar
cycle, vs. 25% for the bipolar cycle. Therefore, differences
of about 1/3 in the ener dissipated during ramp-up can
occur because of the diference in the magnetization state
of the conductor.
3.2 Stability Region
The proposed model implies two conditions for conductor quenching. The first one is that the tightly bunched
strands be filled with helium gas (an energy implication),
and that the conductor current be larger than a given
value (a fraction-of-critical implication.) The data can be
shown with the fraction of critical in the ordinate and the
energy margin in the coordinate.
According to the limiting-current model briefly described above, the instability region would be a box limited by the limiting critical fraction (equal to the fraction
of the conductors that are bunched) and by the critical
energy, represented by the fraction of He boiloff.
4
Tests
There have been three types of experiments [1]. THe first
one has current and field ramping. the second has only
field ramping, and the third one has multiple field ramps.
The experiments were conducted in three sets of sample coils with 27 strands (3 x 3 x 3). The sample coils
were single loop coils with different conductors, a 27 allsuperconducting strand cable, a 27-strand copper hybrid
(one of the wires in each triplet is pure copper) and a
27-strand steel (one wire of the triplets is steel). [11
100.
A
so.
cabes.NQ
Shelium.NO
'.O
70.
h.ium.O
.
.*......
.
,.
.
4,0
.
030.
W
M
NO, hokum
80
U
Figure 4 shows the specific energy into the helium
(higher points) and the specific energy into the conductor
(lower points) for the Cu-hybrid coil. The points indicate,
for each test, the AC energy
Figure 4 shows the calculated value of the AC energy
losses at the time of quench or at the highest field (if
unquenched). Each point corresponds to a different test,
with 23 tests in total. Two cases are shown that indicate
the variation with E: (a) shows the results for E = 0.0005
s, (b) shows the results for E = 0.001 s. If the model is
appropriate and there is a maximum energy that can be
deposited in the helium before the conductor quenches, it
is clear that E) < 0.001 s. Only an upper bound on 9 can
be derived from comparison between the model and the
experiments, due to the fact that coupling losses seem to
be small. The e values estimated here agree well with
measurements [2].
The specific energy into the helium for all the tests analyzed are shown in Figure 5. e has been adjusted for
the other conductors, being E) = 0.0005 s for the steelhybrid and for the all-superconductor coil. The were 21
tests for the hybrid steel conductor, and 28 for the allsuperconductor conductor. The only results that deviate
from the pattern in the last set of runs (all superconductor, tests 57-60 and 65) are due to quenches during the
down ramp and are improperly analyzed in the present
work. It should be noted that the conductor quenches at
high critical fractions.
.
so .
..
0e0 0 0
AA
OAA
...
-
bg*
apt
40-
e- 0.0002 s
20
S10.
0
*o0. h.ilum
N,
A.AA A
520
bl
A N.
40
0
5
10
1520
.
0.
0
25
20
100
90
.
0
heiumNO
10
20
30
40
50
60
70
so
* hofium,O
-
70
0.
C,
so
0
U
0.
0
eeo
-
40
30
*em.e.
e- 0.0013
Figure 5: Same as Figure 3, but showing results for all
sample coils
"o*,
10
0
o
5
10
... ".
15
20
25
Figure 4: Specific energy at quench or highest field (if
unque nched) for the copper-hybrid cable. Each point correspon ds to a different ramp test. Curves have varying
values of (9.
For each sample coil, many different ramp rates and
maximum field/currents were tested. Losses have been
calculated for each ramp rate test. The average energy
densities (specific energy) deposited in the conductor and
in the helium are also evaluated. The time constant E is
determined by the best fit to the data, as described below.
3
The fraction of average helium that is vaporized is
shown in Figure 6. It is very suggestive that once the
average helium gas fraction reaches 3.5%, the conductor
quenches.
The conclusion of this part of the study is that, with the
equations used, when energies of 50 mJ/cm' (theoretically
and experimentally) are deposited in the helium, the tight
strands cease to be superconducting.
4.1 Field ramping, constant current tests
As suggested above, the whether the coil quenches depends both on the energy dissipated and the fraction of
critical. The quench/unquench boundary can be investigated by plotting the results of the tests shown in Figure 5
with the AC loss energy in the coordinate and the fraction
of critical in the ordinate.
conductor sample coil. Figure 8 shows the results with
the current and field ramping, with field ramping (single
ramp), and first ramp-up of multiple cycles cases. Figure 8
shows that about 30% of the strands are tightly bunched
(the boundary falls at about 70% critical, which, following
the arguments above, means that 30% of the strands are
tightly bunched).
0.03 ,
''P
0.025
0
.- o
002
0.01s
SNOQUENCH
0.01
1.000
0.005
000
o0
0.800
0'
0
10
20
30
40
50
60
70
so
to fM r-a
0.600
0
0.400
C
Figure 6: Average helium fraction vaporized in the tests
shown in Figure 4
The results for the steel hybrid cable experiments are
shown in Figure 7. The coordinate shows the fraction of
critical (current) at the time of the quench. Note that
relatively low values of critical fraction, fit - 0.5 are
needed to quench these cables. This implies that a relatively large number of the strands in the region of tight
bundles, about half. If half of the strands quench due to
the AC losses, then the current in the unquenched strands
doubles: with a critical fraction of 0.5, then the current in
these strands exceeds the critical current, and the entire
cable quenches.
1.200
-r
1.000
+
" quench
aN
0.800
A-
0
C
u-..
.3 unquenched
0.600
.-
40
Ia
0.400 +
0
02
0.200
i
i
0.00%
1.00%
0.000
2
1
2.00%
Helium bolloff fraction
Figure 7: Stability/quench region for the steel hybrid sample coil
Note that there are some points well inside of the box,
when the boundaries of the box should be limiting. Possible reason for the relatively large scatter will be described
in Section 4.3.
4.2 Field ramping, constant current tests
A second class of tests were carried in which the field was
ramped with constant conductor current.
The cases of ramped-current and constant current are
compared in this section, for the case of the steel hydrid
4
.2~
LL
B
" DC, quench
4-
13 DC, no quench
0.200
0.000
6.
0.00%
1.00%
2.00%
3.00%
4.00%
Average Helium Boiloff Fraction
Figure 8: Stability/quench boundary for the steel hybrid
conductor with constant current, varying field.
These results tend to confirm that the critical average
helium boiloff is about 3%. independently of whether the
current is ramped or not (for first order, the AC losses are
not dependent on the current ramping, only on field variations). Considering that for these cases the maximum
local heating in the helium is about 6 times larger than
the average, then the maximum local evaporation is 18%.
Since the volume expansion of the helium from the liquid
into the gaseous phase is about 7-8, then the volume in between tightly bunched strands could be occupied entirely
by gaseous helium.
4.3 Premagnetization of the Sample Coil
To better characterize the measurements, it was suggested
to run a half cycle with no current prior to each test.
The tests were combined with the multiple ramp tests.
The results for the first ramp for these tests are shown
in Figure 8. Results indicated that it was more difficult to quench the superconductor (indeed, the conductor quenched only after operating near critical current),
supporting the assumption that premagnetizing the superconductor reduces the dissipation.
However, there was additional energy dissipated in the
conductor during the following ramps, and the model
breaks down, as will be discussed below.
4.4 Multiple Ramps
To test whether the anomalous behaviour of the ICCS is
due to energy rather than power margin, a set of experiments with multiple unipolar ramps of the magnetic field
was designed. The conductor current was DC. Figure 8
shows the results of a calculation for the first ramp-up,
but the field was ramped up and down 25 times. The
figure is calculated assuming bipolar cycle dissipation, so
the results need to be multiplied by a factor that could
be as small as 17/25. Although the energy dissipated per
ramp was not enough to quench the conductor, the model
predicts that the first ramp-down or the second ramp-up
would. Since the dissipated power in the ramp-down is
the same as the energy during the ramp-up, at the end
of the second ramp-down the average helium boiloff is
about 8% x 42%/50% ~ 6%, substantially larger than
the 3 - 4% that is necessary according to the model. Although the superconductor may not quench during the
ramp-down since the fraction of critical is decreasing, it
should quench during the second ramp-up, and it does
not! At the present time, this is important evidence that
the anomalous behaviour may not be due to a low energy
margin.
The superconductor received substantial heat during
the pulses. It is interesting to investigate the heat balance,
as the sample coil did not quench even after 25 cycles.
The radii of the cable and helium is about 2.5 mm and
that of the conduit is 3.1 mm. The energy dissipated
in the conductor, q'" is about 101 W/m 3 (10 mW/cm 3 ).
The minimum q"' that quenches the sample coil, if the
quench is determined by a power limit, is 10' W/m 3
(1 mW/cm 3 )!!!
The total run time was about 250 s (5 s ramp-up and 5
s ramp-down, with 25 cycles). The total energy dissipated
in the conductor is 2.5 J/cm3 , which should quench the
conductor, but it does not.
It could be speculated that the conductor could be
cooled via pool boiling to the helium bath outside the
sample. The typical power that needs to be removed
from the cable is about 1OW/m 2 (1 mW/cm2 ) (assuming that the helium itself does not carry the heat out in
the form of bubbles leaving the conductor). The temperature differential across the 0.6 mm jacket is about
AT - q"Ar/kjaket ~ 10-2 K. For the values being considered, heat transfer is convective and very small temperature differentials (< .1K) are needed. A small degree
of superheat is therefore all that is needed to remove the
heat from the test coil. The superconductor can tolerate
relatively large temperature rises (on the order of K's)
without quenching.
4.5 Energy Margin
The same model described above can be used to determine
the results from the energy margin experiments. If the
current in the strands with high void fraction (once the
small void fraction ceases to be superconducting) exceeds
the critical current, then the entire conductor quenches.
The process can be better understood if we identify
that there are regions with different energy margins. The
region with low void fraction has a low energy margin,
and the high void fraction has a high energy margin.
The region of high energy margin has a helium fraction
larger than the average. It is easy to show that the helium
fraction in the unbunched strands is
FH.,..b = 1 - (1 -
7)
F 1 - FHe,ave
7
1 - Fe,min)
where Y is the fraction of bunched strands. The minimum
5
Ei and maximum E 2 energy margins are then
E,F 0 _emin_
Eia 300 i Fu
1 - FHe,ave
\1 - FH
i
3
mJ/cm
and
2
300
FHe,unb'(1 - FHe,ave Mj/Cm
1 - FHeunb/
E FHeave
3
A simple model was built following the above discussion. The results are shown in Figure 9. It simulates the
results of energy margin. The fraction of the strands that
are tightly bunched in a given cross section, fAunc1ed, is
assumed to be func1ed ~ 25%.
400000
300000
E
E 200000
a
C 100000
0
.
2000
4000
.
6000
..
Conductor current (A)
Figure 9: Calculated energy margin as a function of the
fraction of critical
The factor of 4 decrease in margin, and the relatively
constant energy margin at the high currents, are reassuring. If there is a distribution of bunched fractions and of
degrees of tightness, then the transition would be more
smeared.
The ratio between the energy margins in the
"well-cooled" and "ill-cooled" regimes depends on
FHe,min/FHe,ave, while the limiting current is a function
of fbn.,ed.
5
Relevance to Supercritical Helium
The case of pool boiling has been analyzed above. It was
concluded that when the energy going into the helium exceeded 50 mJ/cm , the tightly bunched conductor would
not be superconducting. The results agreed with the experiments carried out [1]. In this section, the critical energy for supercritical helium is calculated.
Supercritical helium does not have the large change in
volume experienced by the liquid to gas transition, but
it is still substantial. The specific weight of helium at
6 bar is shown in Figure 10. Reduction in the available
enthalpy for cooling could also occur in the liquid phase.
Similarly to the case with phase change, the liquid in the
very tight spaces between conductors will expand due to
the increased heat, and the fluid in the center of the space
will be pushed out, as shown in Figure 1.
35
; 30 t
BEE..
300 T
e U
250
U".
25
20
315 t
a,
U
aa
i
10
mon
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0 0
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150
100 T
a a
50 -
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4
5
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"""""""eno"""
,. ..-
1200
U
7
8
9
10
11
12
^
a
13
4
Heium temperature (K)
5
6
7
8
temperature
10
9
11
12
13
(K)
Figure 10: Specific weight of helium at 6 atmospheres as
a function of temperature
Figure 11: Minimum heat that results in expulsion of cold
coolant from the tight channels
An estimate of the minimum energy required to raise
the temperature of liquid helium in the channels can be
obtained in the following manner: assuming that the helium experiences a volumetric expansion of C = pi/pf,
then the fraction of helium in the channels that needs to
be heated is 1/(. Here pi and pf are the helium densities
at the initial and final temperatures (at constant pressure). The energy required to raise the temperature of
the reduced volume is simply AHpi. When including the
change in volume, the minimum energy density required
to raise the temperature in the tightly bunched section of
the conductor is given by
did not show any tendency to quench, up to the critical current. The results from the premagnetized experiments indicate that the stability for premagnetized cases
increases. Finally, it was not possible to quench the superconductor at fixed current with field ramping until the
conductor current was close to critical.
The cable is cooled by the bath surrounding the sample.
This could be the reason why the superconductor did not
quench with the multiple pulses.
One possible manner to prevent the non-uniform distribution is by braiding the conductor. Both a braided
conductor and a twisted conductor were wound by the
NET team [5]. The model would predict that a uniform
cable would show less anomaly than the non-uniform conductor.
Another possibility is to design to a fraction of critical
that is lower than 1 - r (rq is the fraction of bunched
strands). Then if the tight strands quench, the unbunched
strands still can carry the current without quenching. A
much larger energy margin (E 2) can be obtained this way.
However, the higher value E 2q would still be substantially
smaller than previously calculated, even for supercritical
fluids.
EHe,min = AZHpf
The fact that the enthalpy change is multiplied by the
final density is a surprising result. The corresponding
helium energy input EHe,ave (averaged over the cross section) is then
EHe,ave = Eue,mzn
FHe,min 1 - FHe,aje
1 - FHe,min FHe,ave
Figure 11 shows EHe,ave curve for the case of helium at
6 atmospheres, for FHe,min = 10% and FHe,ave = 40%.
References
Note that after 8 K, EHe,ae saturates. This is due to the
fact that the change in volume more than compensates
for the increase in enthalpy.
If the superconductor current sharing temperature is
(1] Takayasu, M., elsewhere in this conference.
is
[2] Takayasu, M., MIT Plasma Fusion Center, unpublished report (1990)
about 250 mJ/cm (with a corresponding value of energy
margin - 120 mJ/cm' for the tight strands). This value
is about a factor of 5 larger than for pool boiling.
[3] Gung, C-Y, MIT Plasma Fusion Center, unpublished
report (1992)
6
[4] Provided by J. Minervini, MIT Plasma Fusion Center; measurements carried out by NIST
about 7-8 K, then the average helium energy EHe,a,
Discussion
The hypothesis of non-uniform helium distribution as the
reason for the anomaly of ICCS was tested.
Although the initial tests supported the hypothesis, the
latter evidence (multiple ramp rates) points away from an
energy limit as the reason for the ICCS anomalous behaviour. The multiple pulses tests (with ramping field)
6
(5] P. Bruzzone, IEEE Trans Magn 28 190, 1992